In this paper, we show how lazy functional programs can be compiled for the Java Virtual Machine using a mapping between a version of the 〈v, G〉-machine and the Java Virtual Machine. This mapping is elegant – the description is entirely straightforward – and efficient – using it, both code size and execution speed are of the same order of magnitude as those obtained with a traditional functional language bytecode interpreter. In future, our work could serve as the basis of an interface between Haskell and Java.

Recursive block decomposition algorithms (also known as quadtree algorithms when the blocks are all square) have been proposed to solve well-known problems such as matrix addition, multiplication, inversion, determinant computation, block LDU decomposition and Cholesky and QR factorization. Until now, such algorithms have been seen as impractical, since they require leading submatrices of the input matrix to be invertible (which is rarely guaranteed). We show how to randomize an input matrix to guarantee that submatrices meet these requirements, and to make recursive block decomposition methods practical on well-conditioned input matrices. The resulting algorithms are elegant, and we show the recursive programs can perform well for both dense and sparse matrices, although with randomization dense computations seem most practical. By ‘homogenizing’ the input, randomization provides a way to avoid degeneracy in numerical problems that permits simple recursive quadtree algorithms to solve these problems.

We derive a confluent λ-calculus with a catch/throw mechanism (called λct-calculus) from Parigot's λμ-calculus. We also present several translations from one calculus into the other which are morphisms for the reduction. We use them to show that the λct-calculus is a retract of λμ-calculus (these calculi are isomorphic if we consider only convertibility). As a by-product, we obtain the subject reduction property for the λct-calculus, as well as the strong normalization for λct-terms typable in the second order classical natural deduction.

List homomorphisms are functions that are parallelizable using the divide-and-conquer paradigm. We study the problem of finding homomorphic representations of functions in the Bird–Meertens constructive theory of lists, by means of term rewriting and theorem proving techniques. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons- and snoc-lists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. The inductive claim is provable automatically. We illustrate the method and the procedure by the systematic parallelization of the scan-function (parallel prefix) and of the maximum segment sum problem.

Injective pure type systems form a large class of pure type systems for which one can compute by purely syntactic means two sorts elmt(Γ[mid ]M) and sort(Γ[mid ]M), where Γ is a pseudo-context and M is a pseudo-term, and such that for every sort s,

formula here

By eliminating the problematic clause in the (abstraction) rule in favor of constraints over elmt(.[mid ].) and sort(.[mid ].), we provide a sound and complete type-checking algorithm for injective pure type systems. In addition, we prove expansion postponement for a variant of injective pure type systems where the problematic clause in the (abstraction) rule is replaced in favor of constraints over elmt(.[mid ].) and sort(.[mid ].).